Writing a logic for shape coordinates

[mahadevan.swamy]

Hi,

In an excel spreadsheet, I have the coordinates of a small circle and
another shape which is a semi-circle and a rectange together. For
this
shape (semi-circle and rectange), I have the X and Y coordinates and
R
coordinate for the semi-circle. I also have the absolute radius of
this shape measured from (0,0). For the small circle, I am given X,Y,
and R coordinates.


The objective is to check whether the small circle is in the range of
this shape and assign a particular value: "IN", "OUT", or "MID". I
would appreciate if any one can help me build a logic on this. Thanks


Swamy

 

[Joel]

See my thoughts below.


Sub Littlecircle()

'solution
' Check if Little circle is completly outside or completly inside
' otherwise it is it is mid

'Given rectangle width = RectW
'Given rectangle height = RectH
'Rectangle bottom left corner at (RectX,RectY)

'Given Circle on top of rectangle
'Circle Radius = RectW/2
'Center of circle at (X + (RectW/2)), RectH)

'Little circle radius = LittleR
'Little circle location = (LittleX,LittleY)

'first eliminate obvious outside evvents
'Little circle extends beyond bottom of rectangle
If LittleY - LittleR < RectY Then
Results = "Out"
Exit Sub
End If
'Little circle extends beyond left of rectangle
If LittleX - LittleR < RectX Then
Results = "Out"
Exit Sub
End If
'Little circle extends beyond right of rectangle
If LittleX + LittleR > (RectX + RectW) Then
Results = "Out"
Exit Sub
End If
'Next check if little circle is above rectangle
If LittleY > (RectY + RectH) Then

'compute distance from center of semicircle to center little circle
xdistance = LittleX - (RectX + (RectW / 2))
ydistance = LittleY - RectY
distance = Sqr((xdistance * xdistance) + (ydistance * xdistance))

'check if outside circle
If distance > RectW / 2 Then
Results = "Out"
Exit Sub
End If

'check if it is inside semi-circle
If distance + LittleR < (RectW / 2) Then

'make sure Little circle doesn't extend below rectangle
If LittleY - LittleR < RectY Then

Results = "In"
Exit Sub
End If
End If

End If

'Now the only thing to check is if Little circle inside rectangle
'Little circle inside bottom of rectangle
If LittleY - LittleR > RectY Then
Results = "In"
Exit Sub
End If
'Little circle inside left side of rectangle
If LittleX - LittleR > RectX Then
Results = "In"
Exit Sub
End If
'Little circle inside right side of rectangle
If LittleX + LittleR < (RectX + RectW) Then
Results = "In"
Exit Sub
End If

Results = "Mid"

End Sub

 

[mahadevan.swamy]

Thank you for your solution. I am very new to VB and I don't know how
to use your solution. I was hoping to write a small formula to perform
some calculation. I would like to fill you with some details on this
coordinates problem.

I have a big circle which consists of 32 small circles oriented in
different places. These circles are sensors that has to read a part.
When the blueprint of the part is placed on top of these sensors,
these sensors should read the part. This blueprint consists of holes
and slots (rectangle with a semi-circle) in the drawing and where ever
there is a hole or slot on top of the sensor, the sensor should read
0, 1 or X. I want to check if the hole is in the range of the sensor,
the value should be 0. If the hole is out of range, the value should
be 1. If the hole is blocking the sensor or very closely touching the
sensor, the value should be X.

There is a bigger inner hole (pilot bore hole) in the part and all the
small holes (mounting holes, sensor holes etc..) are outside of this
big hole. This big hole has the coordinate (0,0,r) always. Some part
consists of slots which are connected to the bigger inner hole and
slot design is a rectangle with a semi-circle that we were discussing
about. The slot can be oriented at any angle.

There are two kinds of slot. One kind of slot looks like a semi-circle
and a rectangle together that is connected to the pilot bore hole.If
you want a picture of this, I can send it to you. I am given X, Y, and
R coordinate of the semi-circle. I am also given the radius of this
point from (0,0). The other kind of slot looks like a wide rectangle
but is chamfered in the two corners. For this, I am given width of the
rectangle, radius of the chamfer and distance from the end of the slot
to the origin. The slot can be oriented anywhere on the part. I have
another information which may or may not be useful. The mounting holes
(small holes outside bigger inner hole) has a center line radius
measured with respect to the origin and the slot cannot extend beyond
this radius (for the rectangle part). Small part of the semi-circle is
extended beyond this radius but I am not given the dimension of how
much it has been extended.

I have a row that consists of X, Y and R coordinates for each hole in
the part and a list of sensors with their X,Y and R coordinates. I am
trying to build a logic that will help me to see whether the sensor is
in the range of the hole or slot and execute decisions to produce some
results. I would appreciate your help on this. Thanks

Mahadevan Swamy

 

[Joel]

I understand your problems after reading your lastest posting. I'm an
electrical engineer, prgrammer, and have worked a lot with mechanical
engineers. i also have a very strong geometry background.

You need to read the comment in the code I sent you. The comments are more
important than the code. I tried to explain how to solve the problem, not
the actual solution.

It is very hard to figure out if one geometric figure is partially inside
and outside of another geometric figure. it is easier to see if it is
completely inside and completely outside. If it is neither inside or outside
then it must be overlappings.

There isn't a single formula that can be used. and then you problem is more
complicated than I originally thought. First your semicircles radius have
different arc lengths. Second semicircle can be on any side of the rectangle.

as I said in the comments of the code, Check for the 1's and 0's. What is
left is the X's.

I would be glad to assist is this problems. Use my email at work
(e-mail address removed).

Lets take the simple solution first and see if solves the problem. Lets
convert the slots are rectangles. Find the maximum X,Y coordinates and X,Y
position of the slots and check to see if the rectangles can be seen by each
of the sensors.

The problem turnout to be pretty simple. You only have to check the four
corners or a rectangle to see if a rectangle is outside of a larger circle.
It is impossible for a rectangle which is inside a circle to have an edge
outside and all four corners inside.

The proof to this has to do with the shortest distance between 2 points is a
straight line. An edge of a rectange is a straight line and therefore is the
shortest distance. An arc of a circle is not a straight line and therefore
must be longer than the straight line. For an edge of tthe rectangle to be
outside the circle is a contradiction. The arc of the circle would have to
be shorter than the side of the rectangle.

 

[mahadevan.swamy]

There are atleast 1000 parts which consists of different patterns.
Some consists of mounting holes all over the place or mounting holes
and slots. The data structure that I am looking at is that there
should be one column for all part numbers and 32 columns for the 32
sensors. For a certain part design, value 0 will go for sensors that
detects a hole or a slot (uncovered), value 1 goes for sensors that
are covered and value X will go for sensors that are blocked or very
closely touching (blocking) the diameter (it is like an eclipse). In
another worksheet, in one row or one column, I would have the X,Y, and
R coordinates of each hole and some necessary info for the slot hole.
Also when I change the co-ordinates of the sensor, it should give me
accurate information.

The first phase of the problem is complete. The design used in this
problem was that there were mounting holes over the place and no
slots. So, the sensors can read whether the holes are in their range
and assign a value and thus we'll know whether it is covered or not.
Now there is a new design with two types of slot and it is a bit
tricky to figure out a logic. Since you have some good background in
geometry and programing I could use your help. If you need to
visualize what I am talking about, please tell me and I'll send you
the file to your email. Thanks

Mahadevan Swamy

 

[Joel]

Send me the file with instructions. You last reply didn't tell me what I
needed to do.

 

[mahadevan.swamy]

Hi,

I have sent the file to you.

Mahadevan Swamy